Biomedical Engineering Reference
In-Depth Information
Outside
I
Na
R
Na
R
K
I
K
R
Cl
C
m
V
m
-
-
-
E
Na
E
K
E
Cl
+
+
+
Inside
FIGURE 12.15
Circuit model of a small area of the nerve at rest with all of its passive electrical properties. The
Na-K
active pump shown in Figure 12.14 is removed, since it does not contribute electrically to the circuit.
and the lipid bilayer of the membrane is the insulating material (see Figure 12.3). Capaci-
tance for a neuron membrane is approximately 1mF
cm
2
Membrane capacitance implies
that ions do not move through the membrane except through ion channels.
The membrane can be modeled using the circuit in Figure 12.15 by incorporating
membrane capacitance with the electromotive and resistive properties. A consequence
of membrane capacitance is that changes in membrane voltage are not immediate but
follow an exponential time course due to first-order time constant effects. To appreciate
the effect of capacitance, the circuit in Figure 12.15 is reduced to Figure 12.16 by using a
Thevenin's equivalent for the batteries and the resistors with
=
:
and
given in
R
TH
V
TH
Eqs. (12.35) and (12.36).
1
R
TH
¼
ð
12
:
35
Þ
1
R
K
þ
1
R
Na
þ
1
R
Cl
Outside
R
TH
V
m
C
m
-
V
TH
+
Inside
FIGURE 12.16
Th´venin's equivalent circuit of the model in Figure 12.15.
